Cross Validate Strategy
Kevin Lu
October 23, 2017
1. Load Packages
source("./Mean Reversion/RMR.001 Load Packages.R") 2. Load Data
pricing_data <- read_csv("./Mean Reversion/Raw Data/pricing data.csv", col_types = c("iTdddddddci")) 3. Prepare Data Function
Description
Spreads Poloneix pricing data into wide format and filters data to a specified time resolution and time window.
Arguments
pricing_data: A dataframe containing pricing data from Poloneix gathered in tidy format.
time_resolution: The number of seconds that each observation spans. Takes values 300, 900, 1800, 7200, 14400, and 86400.
start_date: The start date of the time window.
end_date: The end date of the time window.
Value
Returns a dataframe consiting of the unix timestamp, date time, and the closing price of various currency pairs.
prepare_data <- function(pricing_data, time_resolution, start_date, end_date) {
df <- pricing_data %>%
filter(period == time_resolution,
date_time >= start_date,
date_time <= end_date) %>%
select(date_unix, date_time, close, currency_pair) %>%
spread(currency_pair, close)
return(df)
} 4. Test Cointegration Function
Description
The Engle-Granger method is used to test for cointegration. This method is comprised of two steps: (1) Perform a linear regression of log(coin_y) on log(coin_x). (2) Perform an Augmented Dickey-Fuller test on the residuals from the linear regression estimated in (1). The ADF test specification is of a non-zero mean, no time-based trend, and one autoregressive lag.
Arguments
coin_y: A vector containing the pricing data for the dependent coin in the regression.
coin_x: A vector containing the pricing data for the independent coin in the regression.
Value
Returns the ADF test statistic for the given coin pair.
test_cointegration <- function(coin_y, coin_x) {
lm_model <- lm.fit(y = log(coin_y), x = cbind(1, log(coin_x)))
lm_residuals <- lm_model[["residuals"]]
adf_test <- ur.df(lm_residuals, type = "drift", lags = 1)
df_stat = adf_test@testreg[["coefficients"]][2, 3]
return(df_stat)
} 5. Create Coin Pairs Function
Description
Two sets of currency pairs are examined: currency pairs where USDT is the quote currency and currency pairs where BTC is the quote currency. All combinations of coins are created within a given quote currency. Combinations that consist of the coin with itself are removed.
Arguments
quote_currency: A string indicating the quote currency of the currency pairs. Can take values USDT or BTC.
Value
Returns a dataframe containing the coin pairs.
create_pairs <- function(quote_currency) {
if (quote_currency == "USDT") {
coin_list <- c("USDT_BTC", "USDT_DASH", "USDT_ETH", "USDT_LTC", "USDT_REP", "USDT_XMR", "USDT_ZEC")
}
if (quote_currency == "BTC") {
coin_list <- c("BTC_DASH", "BTC_ETH", "BTC_LTC", "BTC_REP", "BTC_XEM", "BTC_XMR", "BTC_ZEC")
}
coin_pairs <- expand.grid(coin_list, coin_list) %>%
rename(coin_y = Var1,
coin_x = Var2) %>%
filter(coin_y != coin_x) %>%
mutate_if(is.factor, as.character) %>%
as_tibble()
return(coin_pairs)
} 6. Test Coin Pairs Function
Description
Test for cointegration between each coin pair generated by the create_pairs() function. The test for cointegration is performed by test_cointegration().
Arguments
train: A dataframe generated by prepare_data() that represents the training set for the coin pairs.
coin_pairs: A dataframe generated by create_pairs().
Value
Returns a dataframe containing the coin pairs and the ADF test statistic resulting from testing cointegration between each coin pair.
test_pairs <- function(train, coin_pairs) {
adf_stat <- numeric(nrow(coin_pairs))
for (n in 1:nrow(coin_pairs)) {
coin_y <- coin_pairs[[n, "coin_y"]]
coin_x <- coin_pairs[[n, "coin_x"]]
cointegration_results <- test_cointegration(coin_y = train[[coin_y]], coin_x = train[[coin_x]])
adf_stat[n] <- cointegration_results
}
df <- coin_pairs %>%
mutate(adf_stat = adf_stat) %>%
arrange(adf_stat)
return(df)
} 7. Select Coin Pairs Function
Description
Select cointegrated coin pairs to be used in a mean reversion strategy. Coin pairs are tested for cointegration using test_pairs(). Coin pairs with an ADF test statistic below a certain threshold are selected.
Arguments
train: A dataframe generated by prepare_data() that represents the training set for the coin pair.
coin_pairs: A dataframe generated by create_pairs().
Value
Returns a dataframe containing the coin pairs that were selected.
select_pairs <- function(train, coin_pairs) {
df <- test_pairs(train = train, coin_pairs = coin_pairs) %>%
filter(adf_stat <= -3.43)
return(df)
} 8. Train Model Function
Description
Performs rolling linear regression of log(coin y) on log(coin x) using a defined rolling window length over the test set.
Arguments
train: A dataframe generated by prepare_data() that represents the training set for the coin pair.
test: A dataframe generated by prepare_data() that represents the test set for the coin pair.
coin_y: A string indicating the dependent coin in the coin pair regression.
coin_x: A string indicating the independent coin in the coin pair regression.
rolling_window: The number of observations used in each iteration of a rolling linear regression.
Value
Returns a list containing the intercept and hedge ratio calculated from a rolling regression over the test set as well as the spread and z-score of the spread.
train_model <- function(train, test, coin_y, coin_x, rolling_window) {
# Perform rolling linear regression for the test set
rolling_coef <- bind_rows(train, test) %>%
mutate(y = log(.[[coin_y]]),
x = log(.[[coin_x]])) %>%
select(y, x) %>%
rollapply(data = .,
width = rolling_window,
FUN = function(df) {
df <- as_tibble(df)
model <- lm.fit(y = df[["y"]], x = cbind(1, (df[["x"]])))
return(model[["coefficients"]])},
by.column = FALSE,
fill = NA,
align = "right") %>%
as_tibble() %>%
rename(intercept = x1,
hedge_ratio = x2) %>%
filter(row_number() > nrow(train))
# Calculate spread in training and test set
train <- train %>%
mutate(spread = lm.fit(y = log(train[[coin_y]]), x = cbind(1, log(train[[coin_x]])))[["residuals"]])
test <- test %>%
mutate(spread = log(test[[coin_y]]) - log(test[[coin_x]]) * rolling_coef[["hedge_ratio"]] - rolling_coef[["intercept"]])
# Combine train and test to calculate rolling z-score for the test set
result <- bind_rows(train %>% mutate(source = "train"),
test %>% mutate(source = "test")) %>%
mutate(rolling_mean = roll_mean(spread, n = rolling_window, fill = NA, align = "right"),
rolling_sd = roll_sd(spread, n = rolling_window, fill = NA, align = "right"),
spread_z = (spread - rolling_mean) / rolling_sd) %>%
filter(source == "test")
# Return list of statistics for the test set
return(list(intercept = rolling_coef[["intercept"]],
hedge_ratio = rolling_coef[["hedge_ratio"]],
spread = result[["spread"]],
spread_z = result[["spread_z"]]))
} 9. Generate Signals Function
Description
Generate trading signals that indicate the current position in the spread formed by a trained model generated by
train_model(). The trained model generates the spread and z-score of the spread over the test set. A signal of +1 indicates a long position in the spread, 0 indicates a flat position, and -1 indicates a short position in the spread.
Arguments
train: A dataframe generated by prepare_data() that represents the training set for the coin pair.
test: A dataframe generated by prepare_data() that represents the test set for the coin pair.
coin_y: A string indicating the dependent coin in the coin pair regression.
coin_x: A string indicating the independent coin in the coin pair regression.
model: A trained model generated by train_model().
Value
Returns a vector containing the trading signal over the test set.
generate_signals <- function(train, test, coin_y, coin_x, model) {
df_signals <- test %>%
mutate(spread = model[["spread"]],
spread_z = model[["spread_z"]],
lag_spread_z = lag(spread_z, 1, default = 0),
signal_long = if_else(lag_spread_z <= 0.0 & lag_spread_z > -1.0, 0.25, 0),
signal_long = if_else(lag_spread_z <= -1.0 & lag_spread_z > -2.0, 0.50, signal_long),
signal_long = if_else(lag_spread_z <= -2.0 & lag_spread_z > -3.0, 0.75, signal_long),
signal_long = if_else(lag_spread_z <= -3.0 & lag_spread_z > -4.0, 1.00, signal_long),
signal_long = if_else(lag_spread_z <= -4.0 & lag_spread_z > -5.0, 1.00, signal_long),
signal_long = if_else(lag_spread_z <= -5.0 & lag_spread_z > -6.0, 1.00, signal_long),
signal_long = if_else(lag_spread_z <= -6.0 & lag_spread_z > -7.0, 0.00, signal_long),
signal_long = if_else(lag_spread_z <= -6.0, 0, signal_long),
signal_short = if_else(lag_spread_z >= 0.0 & lag_spread_z < 1.0, -0.25, 0),
signal_short = if_else(lag_spread_z >= 1.0 & lag_spread_z < 2.0, -0.50, signal_short),
signal_short = if_else(lag_spread_z >= 2.0 & lag_spread_z < 3.0, -0.75, signal_short),
signal_short = if_else(lag_spread_z >= 3.0 & lag_spread_z < 4.0, -1.00, signal_short),
signal_short = if_else(lag_spread_z >= 4.0 & lag_spread_z < 5.0, -1.00, signal_short),
signal_short = if_else(lag_spread_z >= 5.0 & lag_spread_z < 6.0, -1.00, signal_short),
signal_short = if_else(lag_spread_z >= 6.0 & lag_spread_z < 7.0, -0.00, signal_short),
signal_short = if_else(lag_spread_z >= 6.0, 0, signal_short),
signal = signal_long + signal_short,
signal = if_else(is.na(signal), 0, signal),
signal = if_else(cummin(lag_spread_z) <= -6.0, 0, signal),
signal = if_else(cummax(lag_spread_z) >= 6.0, 0, signal))
return(df_signals[["signal"]])
} 10. Backtest Pair Function
Description
Calculate the return of a cointegration-based mean reversion trading strategy using coin y and coin x.
The current backtesting logic uses a model generated by train_model() and trading signals generated by generate_signals(). The coin_y_return and coin_x_return indicate the one period percentage return of each coin. The coin_y_position and coin_x_position indicate the market value in USD in each coin. coin_y_pnl and coin_x_pnl indicate the USD value of the profit and loss for each coin. The combined_position indicates the gross market value of the combined positions. The return is calculated relative to the maximum capital allocation to the given coin pair.
Arguments
train: A dataframe generated by prepare_data() that represents the training set for the coin pair.
test: A dataframe generated by prepare_data() that represents the test set for the coin pair.
coin_y: A string indicating the dependent coin in the coin pair regression.
coin_x: A string indicating the independent coin in the coin pair regression.
rolling_window: The number of observations used in each iteration of a rolling linear regression.
Value
Returns a vector containing the cumulative return of applying the trading strategy to the given coin pair.
backtest_pair <- function(train, test, coin_y, coin_x, rolling_window) {
model <- train_model(train = train,
test = test,
coin_y = coin_y,
coin_x = coin_x,
rolling_window = rolling_window)
df_backtest <- test %>%
mutate(signal = generate_signals(train = train,
test = test,
coin_y = coin_y,
coin_x = coin_x,
model = model),
coin_y_return = test[[coin_y]] / lag(test[[coin_y]], 1) - 1,
coin_x_return = test[[coin_x]] / lag(test[[coin_x]], 1) - 1,
coin_y_position = signal * 1 * 1,
coin_x_position = signal * model[["hedge_ratio"]] * -1,
coin_y_pnl = lag(coin_y_position, 1) * coin_y_return,
coin_x_pnl = lag(coin_x_position, 1) * coin_x_return,
combined_position = abs(coin_y_position) + abs(coin_x_position),
combined_pnl = coin_y_pnl + coin_x_pnl,
combined_return = combined_pnl / (1 + abs(model[["hedge_ratio"]]))) %>%
mutate_all(funs(ifelse(is.na(.), 0, .))) %>%
mutate(return_pair = cumprod(1 + combined_return))
return(df_backtest[["return_pair"]])
} 11. Backtest Strategy Function
Description
Calculate the return of a cointegration-based mean reversion trading strategy using an equally weighted portfolio of cointegrated coin pairs. The cumulative return of each coin pair is calculated using return_pair() and the mean is taken.
Arguments
train: A dataframe generated by prepare_data() that represents the training set for the coin pair.
test: A dataframe generated by prepare_data() that represents the test set for the coin pair.
selected_pairs: A dataframe generated by select_coins() that represents a set of cointegrated coin pairs.
rolling_window: The number of observations used in each iteration of a rolling linear regression.
Value
A vector containing the cumulative return of the overall trading strategy.
backtest_strategy <- function(train, test, selected_pairs, rolling_window) {
if (nrow(selected_pairs) == 0) {
return(1)
}
df <- tibble()
for (i in 1:nrow(selected_pairs)) {
single_pair <- tibble(
return_pair = backtest_pair(train = train,
test = test,
coin_y = selected_pairs[["coin_y"]][i],
coin_x = selected_pairs[["coin_x"]][i],
rolling_window = rolling_window),
coin_y = selected_pairs[["coin_y"]][i],
coin_x = selected_pairs[["coin_x"]][i],
date_time = test[["date_time"]]
)
df <- bind_rows(df, single_pair)
}
df <- df %>%
group_by(date_time) %>%
summarise(return_strategy = mean(return_pair))
return(df[["return_strategy"]])
} 12. Plot Single Function
Description
Create plots of a cointegration-based mean reversion trading strategy of a single coin pair conprised of coin y and coin x. There are two plots created by this function. The first plot displays the spread transformed into z-score with three red lines at -2, 0, and 2. A green line indicates the signal which can take values -1, 0, and +1. The second plot displays the cumulative return of the model in blue. Two additional lines show the buy and hold return of coin y and coin x as red and green lines, respectively.
Arguments
train: A dataframe generated by prepare_data() that represents the training set for the coin pair.
test: A dataframe generated by prepare_data() that represents the test set for the coin pair.
coin_y: A string indicating the dependent coin in the coin pair regression.
coin_x: A string indicating the independent coin in the coin pair regression.
rolling_window: The number of observations used in each iteration of a rolling linear regression.
Value
Prints the plots described above.
plot_single <- function(train, test, coin_y, coin_x, rolling_window) {
model <- train_model(train = train,
test = test,
coin_y = coin_y,
coin_x = coin_x,
rolling_window = rolling_window)
df_plot <- test %>%
mutate(spread = model[["spread"]],
spread_z = model[["spread_z"]],
signal = generate_signals(train = train,
test = test,
coin_y = coin_y,
coin_x = coin_x,
model = model),
return_pair = backtest_pair(train = train,
test = test,
coin_y = coin_y,
coin_x = coin_x,
rolling_window = rolling_window),
return_buyhold_y = test[[coin_y]] / test[[coin_y]][1],
return_buyhold_x = test[[coin_x]] / test[[coin_x]][1])
print(ggplot(df_plot, aes(x = date_time)) +
geom_line(aes(y = spread_z, colour = "Spread Z"), size = 1) +
geom_line(aes(y = signal, colour = "Signal"), size = 0.5) +
geom_hline(yintercept = 0, colour = "red", alpha = 0.5) +
geom_hline(yintercept = 2, colour = "red", alpha = 0.5) +
geom_hline(yintercept = -2, colour = "red", alpha = 0.5) +
scale_color_manual(name = "Series",
values = c("Spread Z" = "blue",
"Signal" = "green")) +
labs(title = "Spread vs Trading Signal",
subtitle = str_c(coin_y, " and ", coin_x),
x = "Date",
y = "Spread and Signal"))
print(ggplot(df_plot, aes(x = date_time)) +
geom_line(aes(y = return_pair, colour = "Model"), size = 1) +
geom_line(aes(y = return_buyhold_y, colour = "Coin Y"), size = 0.5, alpha = 0.4) +
geom_line(aes(y = return_buyhold_x, colour = "Coin X"), size = 0.5, alpha = 0.4) +
geom_hline(yintercept = 1, colour = "black") +
scale_color_manual(name = "Return",
values = c("Model" = "darkblue",
"Coin Y" = "darkred",
"Coin X" = "darkgreen")) +
labs(title = "Model Return vs Buy Hold Return",
subtitle = str_c(coin_y, " and ", coin_x),
x = "Date",
y = "Cumulative Return"))
} 13. Plot Many Function
Description
Create many plots by calling the plot_single() function multiple times. Also creates a plot showing the results of the overall strategy using backtest_strateg(). Creates a train and test set surrounding a cutoff date and creates plot for the top n coins ranked by their ADF statistic.
Arguments
pricing_data: A dataframe containing pricing data from Poloneix gathered in tidy format.
time_resolution: The number of seconds that each observation spans. Takes values 300, 900, 1800, 7200, 14400, and 86400.
cutoff_date: A data representing the cutoff date between the train and test sets.
train_window: A period object from lubridate representing the length of time the train set covers.
test_window: A period object from lubridate representing the length of time the the test set covers. quote_currency: A string indicating the quote currency of the currency pairs. Can take values USDT or BTC.
rolling_window: The number of observations used in each iteration of a rolling linear regression.
number_pairs: The number of pairs to generate plots for.
Value
Prints the plots described above.
plot_many <- function(pricing_data, time_resolution, cutoff_date, train_window,
test_window, quote_currency, rolling_window, number_pairs) {
train <- prepare_data(pricing_data = pricing_data,
time_resolution = time_resolution,
start_date = as.Date(cutoff_date) - train_window,
end_date = as.Date(cutoff_date))
test <- prepare_data(pricing_data = pricing_data,
time_resolution = time_resolution,
start_date = as.Date(cutoff_date),
end_date = as.Date(cutoff_date) + test_window)
coin_pairs <- create_pairs(quote_currency = quote_currency)
selected_pairs <- select_pairs(train = train,
coin_pairs = coin_pairs)
if (nrow(selected_pairs) == 0) {
return("No coin pairs selected.")
}
print(selected_pairs)
for (i in 1:min(number_pairs, nrow(selected_pairs))) {
plot_single(train = train,
test = test,
coin_y = selected_pairs[["coin_y"]][i],
coin_x = selected_pairs[["coin_x"]][i],
rolling_window = rolling_window)
}
test <- test %>%
mutate(return_strategy = backtest_strategy(train = train,
test = .,
selected_pairs = selected_pairs,
rolling_window = rolling_window))
ggplot(test, aes(x = date_time)) +
geom_line(aes(y = return_strategy, colour = "Strategy"), size = 1) +
geom_line(aes(y = USDT_BTC / USDT_BTC[1], colour = "USDT_BTC"), size = 0.5, alpha = 0.4) +
geom_hline(yintercept = 1, colour = "black") +
scale_color_manual(name = "Return",
values = c("Strategy" = "darkblue",
"USDT_BTC" = "darkred")) +
labs(title = "Strategy Return vs Buy Hold Return",
x = "Date",
y = "Cumulative Return")
} 14. Set Parameters
time_resolution <- 900
train_window <- days(32)
test_window <- days(16)
quote_currency <- "USDT"
rolling_window <- 86400 / time_resolution * as.numeric(days(2)) / 86400
number_pairs <- 3
test_by <- "16 days" 15. Cross Validation September 2017
plot_many(pricing_data = pricing_data,
time_resolution = time_resolution,
cutoff_date = "2017-09-01",
train_window = train_window,
test_window = test_window,
quote_currency = quote_currency,
rolling_window = rolling_window,
number_pairs = number_pairs)## # A tibble: 3 x 3
## coin_y coin_x adf_stat
## <chr> <chr> <dbl>
## 1 USDT_REP USDT_ZEC -5.340746
## 2 USDT_ZEC USDT_REP -5.282765
## 3 USDT_REP USDT_ETH -3.471493
16. Cross Validation August 2017
plot_many(pricing_data = pricing_data,
time_resolution = time_resolution,
cutoff_date = "2017-08-01",
train_window = train_window,
test_window = test_window,
quote_currency = quote_currency,
rolling_window = rolling_window,
number_pairs = number_pairs)## # A tibble: 8 x 3
## coin_y coin_x adf_stat
## <chr> <chr> <dbl>
## 1 USDT_ETH USDT_ZEC -4.462054
## 2 USDT_ZEC USDT_REP -4.361885
## 3 USDT_REP USDT_ZEC -4.335836
## 4 USDT_ZEC USDT_ETH -4.290393
## 5 USDT_DASH USDT_XMR -4.016416
## 6 USDT_XMR USDT_DASH -4.000072
## 7 USDT_ETH USDT_REP -3.695401
## 8 USDT_REP USDT_ETH -3.464286
17. Cross Validation July 2017
plot_many(pricing_data = pricing_data,
time_resolution = time_resolution,
cutoff_date = "2017-07-01",
train_window = train_window,
test_window = test_window,
quote_currency = quote_currency,
rolling_window = rolling_window,
number_pairs = number_pairs)## # A tibble: 8 x 3
## coin_y coin_x adf_stat
## <chr> <chr> <dbl>
## 1 USDT_REP USDT_XMR -5.734962
## 2 USDT_XMR USDT_REP -5.685226
## 3 USDT_BTC USDT_REP -4.539502
## 4 USDT_REP USDT_BTC -4.485586
## 5 USDT_BTC USDT_XMR -4.190621
## 6 USDT_XMR USDT_BTC -4.063350
## 7 USDT_DASH USDT_ZEC -3.551029
## 8 USDT_DASH USDT_LTC -3.535247
18. Cross Validation June 2017
plot_many(pricing_data = pricing_data,
time_resolution = time_resolution,
cutoff_date = "2017-06-01",
train_window = train_window,
test_window = test_window,
quote_currency = quote_currency,
rolling_window = rolling_window,
number_pairs = number_pairs)## # A tibble: 14 x 3
## coin_y coin_x adf_stat
## <chr> <chr> <dbl>
## 1 USDT_REP USDT_DASH -6.302270
## 2 USDT_DASH USDT_REP -6.164980
## 3 USDT_DASH USDT_ZEC -4.838517
## 4 USDT_REP USDT_ZEC -4.765335
## 5 USDT_ZEC USDT_DASH -4.419407
## 6 USDT_DASH USDT_XMR -4.338766
## 7 USDT_REP USDT_XMR -4.334303
## 8 USDT_XMR USDT_DASH -4.299602
## 9 USDT_ZEC USDT_REP -4.132672
## 10 USDT_XMR USDT_REP -4.062863
## 11 USDT_XMR USDT_ZEC -3.974349
## 12 USDT_DASH USDT_ETH -3.746119
## 13 USDT_XMR USDT_ETH -3.539918
## 14 USDT_ZEC USDT_XMR -3.518425
19. Cross Validation May 2017
plot_many(pricing_data = pricing_data,
time_resolution = time_resolution,
cutoff_date = "2017-05-01",
train_window = train_window,
test_window = test_window,
quote_currency = quote_currency,
rolling_window = rolling_window,
number_pairs = number_pairs) ## # A tibble: 23 x 3
## coin_y coin_x adf_stat
## <chr> <chr> <dbl>
## 1 USDT_LTC USDT_DASH -5.247891
## 2 USDT_LTC USDT_BTC -5.055356
## 3 USDT_REP USDT_ETH -4.910632
## 4 USDT_DASH USDT_ZEC -4.609111
## 5 USDT_DASH USDT_ETH -4.531939
## 6 USDT_LTC USDT_ETH -4.516577
## 7 USDT_XMR USDT_ZEC -4.484302
## 8 USDT_LTC USDT_ZEC -4.362703
## 9 USDT_DASH USDT_REP -4.351660
## 10 USDT_REP USDT_DASH -4.303321
## # ... with 13 more rows
plot_many(pricing_data = pricing_data,
time_resolution = time_resolution,
cutoff_date = "2017-05-15",
train_window = train_window,
test_window = test_window,
quote_currency = quote_currency,
rolling_window = rolling_window,
number_pairs = number_pairs)## # A tibble: 17 x 3
## coin_y coin_x adf_stat
## <chr> <chr> <dbl>
## 1 USDT_DASH USDT_ZEC -7.181604
## 2 USDT_ZEC USDT_DASH -7.104415
## 3 USDT_ZEC USDT_ETH -5.300897
## 4 USDT_REP USDT_ZEC -5.216806
## 5 USDT_DASH USDT_REP -5.214211
## 6 USDT_ZEC USDT_REP -5.169008
## 7 USDT_REP USDT_DASH -5.159208
## 8 USDT_ETH USDT_ZEC -5.077258
## 9 USDT_DASH USDT_ETH -4.360553
## 10 USDT_REP USDT_ETH -4.194988
## 11 USDT_ETH USDT_DASH -3.964114
## 12 USDT_ETH USDT_REP -3.851741
## 13 USDT_XMR USDT_LTC -3.732961
## 14 USDT_XMR USDT_ETH -3.729675
## 15 USDT_ZEC USDT_XMR -3.703470
## 16 USDT_ETH USDT_XMR -3.683674
## 17 USDT_LTC USDT_XMR -3.629185
20. Cross Validation April 2017
plot_many(pricing_data = pricing_data,
time_resolution = time_resolution,
cutoff_date = "2017-04-01",
train_window = train_window,
test_window = test_window,
quote_currency = quote_currency,
rolling_window = rolling_window,
number_pairs = number_pairs)## # A tibble: 6 x 3
## coin_y coin_x adf_stat
## <chr> <chr> <dbl>
## 1 USDT_BTC USDT_ZEC -3.921811
## 2 USDT_ZEC USDT_BTC -3.894445
## 3 USDT_DASH USDT_XMR -3.786044
## 4 USDT_XMR USDT_DASH -3.627830
## 5 USDT_XMR USDT_ZEC -3.562814
## 6 USDT_ZEC USDT_XMR -3.508866
21. Cross Validation March 2017
plot_many(pricing_data = pricing_data,
time_resolution = time_resolution,
cutoff_date = "2017-03-01",
train_window = train_window,
test_window = test_window,
quote_currency = quote_currency,
rolling_window = rolling_window,
number_pairs = number_pairs) ## # A tibble: 12 x 3
## coin_y coin_x adf_stat
## <chr> <chr> <dbl>
## 1 USDT_LTC USDT_ZEC -4.204591
## 2 USDT_XMR USDT_BTC -4.108816
## 3 USDT_XMR USDT_LTC -4.039288
## 4 USDT_LTC USDT_REP -3.989227
## 5 USDT_XMR USDT_DASH -3.973108
## 6 USDT_LTC USDT_XMR -3.948913
## 7 USDT_XMR USDT_ETH -3.862021
## 8 USDT_LTC USDT_ETH -3.852363
## 9 USDT_XMR USDT_ZEC -3.813835
## 10 USDT_LTC USDT_DASH -3.712336
## 11 USDT_XMR USDT_REP -3.697045
## 12 USDT_LTC USDT_BTC -3.596645
plot_many(pricing_data = pricing_data,
time_resolution = time_resolution,
cutoff_date = "2017-03-15",
train_window = train_window,
test_window = test_window,
quote_currency = quote_currency,
rolling_window = rolling_window,
number_pairs = number_pairs)## # A tibble: 14 x 3
## coin_y coin_x adf_stat
## <chr> <chr> <dbl>
## 1 USDT_LTC USDT_REP -5.797087
## 2 USDT_LTC USDT_ETH -5.559206
## 3 USDT_LTC USDT_XMR -5.547670
## 4 USDT_LTC USDT_BTC -5.212817
## 5 USDT_LTC USDT_DASH -4.969545
## 6 USDT_LTC USDT_ZEC -4.934673
## 7 USDT_XMR USDT_REP -4.924900
## 8 USDT_REP USDT_XMR -4.899259
## 9 USDT_REP USDT_LTC -4.221165
## 10 USDT_BTC USDT_LTC -3.955425
## 11 USDT_XMR USDT_LTC -3.922512
## 12 USDT_ETH USDT_LTC -3.824949
## 13 USDT_REP USDT_ETH -3.620907
## 14 USDT_ETH USDT_REP -3.534860
22. Cross Validation February 2017
plot_many(pricing_data = pricing_data,
time_resolution = time_resolution,
cutoff_date = "2017-02-01",
train_window = train_window,
test_window = test_window,
quote_currency = quote_currency,
rolling_window = rolling_window,
number_pairs = number_pairs)## # A tibble: 7 x 3
## coin_y coin_x adf_stat
## <chr> <chr> <dbl>
## 1 USDT_REP USDT_ETH -4.735592
## 2 USDT_REP USDT_DASH -4.488778
## 3 USDT_REP USDT_BTC -4.291817
## 4 USDT_REP USDT_XMR -4.282674
## 5 USDT_REP USDT_ZEC -4.263626
## 6 USDT_REP USDT_LTC -4.182799
## 7 USDT_LTC USDT_XMR -3.660178
23. Cross Validation January 2017
plot_many(pricing_data = pricing_data,
time_resolution = time_resolution,
cutoff_date = "2017-01-01",
train_window = train_window,
test_window = test_window,
quote_currency = quote_currency,
rolling_window = rolling_window,
number_pairs = number_pairs)## # A tibble: 10 x 3
## coin_y coin_x adf_stat
## <chr> <chr> <dbl>
## 1 USDT_REP USDT_ETH -5.179556
## 2 USDT_REP USDT_XMR -4.969760
## 3 USDT_REP USDT_ZEC -4.911000
## 4 USDT_REP USDT_LTC -4.743256
## 5 USDT_REP USDT_BTC -4.470370
## 6 USDT_REP USDT_DASH -4.430406
## 7 USDT_ETH USDT_REP -3.687047
## 8 USDT_LTC USDT_XMR -3.637524
## 9 USDT_BTC USDT_XMR -3.571980
## 10 USDT_XMR USDT_BTC -3.476249
24. Cross Validation Full
cutoff_dates <- seq(ymd("2017-01-01"), ymd("2017-10-01"), by = test_by)
results <- tibble()
for (i in cutoff_dates) {
i <- as.Date(i)
print(str_c("Cross validating strategy."))
print(str_c("Using train set from ", i - train_window , " to ", i, "."))
print(str_c("Using test set from ", i, " to ", i + test_window, "."))
train <- prepare_data(pricing_data = pricing_data,
time_resolution = time_resolution,
start_date = i - train_window,
end_date = i)
test <- prepare_data(pricing_data = pricing_data,
time_resolution = time_resolution,
start_date = i,
end_date = i + test_window)
coin_pairs <- create_pairs(quote_currency = quote_currency)
test <- test %>%
mutate(return_strategy = backtest_strategy(train = train,
test = test,
selected_pairs = select_pairs(train = train, coin_pairs = coin_pairs),
rolling_window = rolling_window),
return_strategy_change = return_strategy / lag(return_strategy, 1) - 1) %>%
mutate_all(funs(ifelse(is.na(.), 0, .)))
results <- bind_rows(results, test)
} ## [1] "Cross validating strategy."
## [1] "Using train set from 2016-11-30 to 2017-01-01."
## [1] "Using test set from 2017-01-01 to 2017-01-17."
## [1] "Cross validating strategy."
## [1] "Using train set from 2016-12-16 to 2017-01-17."
## [1] "Using test set from 2017-01-17 to 2017-02-02."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-01-01 to 2017-02-02."
## [1] "Using test set from 2017-02-02 to 2017-02-18."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-01-17 to 2017-02-18."
## [1] "Using test set from 2017-02-18 to 2017-03-06."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-02-02 to 2017-03-06."
## [1] "Using test set from 2017-03-06 to 2017-03-22."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-02-18 to 2017-03-22."
## [1] "Using test set from 2017-03-22 to 2017-04-07."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-03-06 to 2017-04-07."
## [1] "Using test set from 2017-04-07 to 2017-04-23."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-03-22 to 2017-04-23."
## [1] "Using test set from 2017-04-23 to 2017-05-09."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-04-07 to 2017-05-09."
## [1] "Using test set from 2017-05-09 to 2017-05-25."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-04-23 to 2017-05-25."
## [1] "Using test set from 2017-05-25 to 2017-06-10."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-05-09 to 2017-06-10."
## [1] "Using test set from 2017-06-10 to 2017-06-26."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-05-25 to 2017-06-26."
## [1] "Using test set from 2017-06-26 to 2017-07-12."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-06-10 to 2017-07-12."
## [1] "Using test set from 2017-07-12 to 2017-07-28."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-06-26 to 2017-07-28."
## [1] "Using test set from 2017-07-28 to 2017-08-13."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-07-12 to 2017-08-13."
## [1] "Using test set from 2017-08-13 to 2017-08-29."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-07-28 to 2017-08-29."
## [1] "Using test set from 2017-08-29 to 2017-09-14."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-08-13 to 2017-09-14."
## [1] "Using test set from 2017-09-14 to 2017-09-30."
## [1] "Cross validating strategy."
## [1] "Using train set from 2017-08-29 to 2017-09-30."
## [1] "Using test set from 2017-09-30 to 2017-10-16."results <- results %>%
mutate(return_strategy_cumulative = cumprod(1 + return_strategy_change),
date_time = as.POSIXct(date_time, origin = "1970-01-01"))
ggplot(results, aes(x = date_time)) +
geom_line(aes(y = return_strategy_cumulative), colour = "blue", size = 1) +
geom_hline(yintercept = 1, colour = "black") +
labs(title = "Strategy Return vs Buy Hold Return", x = "Date", y = "Cumulative Return") 
print(results[["return_strategy_cumulative"]][nrow(results)]) ## [1] 1.713087